viscosity definition essay

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Viscosity Definition and Examples

By definition, viscosity is a fluid’s resistance to flow or deformation. A fluid with a high viscosity, such as honey, flows as a slower rate than a less viscous fluid, such as water. The word “viscosity” comes from the Latin word for mistletoe, viscum . Mistletoe berries yield a viscous glue, also called viscum. Common symbols for viscosity include the Greek letter mu (μ) and the Greek letter eta (η). The reciprocal of viscosity is fluidity .

• Viscosity is a fluid’s resistance to flow.
• Liquid viscosity decreases as temperature increases.
• Gas viscosity increases as temperature increases.

Viscosity Units

The SI unit for viscosity is newton-second per square meter (N·s/m 2 ). However, you’ll often see viscosity expressed in terms of pascal-second (Pa·s), kilogram per meter per second (kg·m −1 ·s −1 ), poise (P or g·cm −1 ·s −1  = 0.1 Pa·s) or centipoise (cP). This makes the viscosity of water at 20 °C about 1 cP or 1 mPa·s.

In American and British engineering, another common unit is pound-seconds per square foot (lb·s/ft 2 ). An alternative and equivalent unit is pound-force-seconds per square foot (lbf·s/ft 2 ).

How Viscosity Works

Viscosity is friction between fluid molecules. As with friction between solids , higher viscosity means it takes more energy to make a fluid flow.

When you pour a liquid from a container, there is friction between the container wall and the molecules. Basically, these molecules stick to the surface to a greater or lesser degree. Meanwhile, molecules further from the surface are more free to flow. They are only inhibited by their interactions with one another. Viscosity looks at the difference in the rate of flow or deformation between between molecules a certain distance from a surface and those at the liquid-surface interface.

Multiple factors influence viscosity. These include temperature, pressure, and the addition of other molecules. The effect of pressure on liquids is small and often ignored. The effect of adding molecules can be significant. For example, adding sugar to water makes it much more viscous.

But, temperature has the greatest effect on viscosity. In a liquid, increasing temperature decreases viscosity because heat gives molecules enough energy to overcome intermolecular attraction. Gases also have viscosity, but the effect of temperature is just the opposite. Increasing gas temperature increases viscosity. This is because intermolecular attraction doesn’t play a significant role in gas viscosity, but increasing temperature leads to more collisions between molecules.

Dynamic Viscosity vs Kinematic Viscosity

There are two ways to report viscosity. Absolute or dynamic viscosity is a measure of a fluid’s resistance to flow while kinematic viscosity is the ratio of dynamic viscosity to a fluid’s density. While the relationship is straightforward, it’s important to remember two fluids with the same dynamic viscosity values may have different densities and thus difference kinematic viscosity values. And, of course, dynamic viscosity and kinematic viscosity have different units.

Table of Viscosity Values

Viscosity of water.

The dynamic viscosity of water is 1.0016 millipascals⋅second or 1.0 centipoise (cP) at 20 °C. Its kinematic viscosity is 1.0023 cSt, 1.0023×10 -6 m 2 /s, or 1.0789×10 -5 ft 2 /s.

Liquid water viscosity decreases as temperature increases. The effect is fairly dramatic. For example, water’s viscosity at 80 °C is 0.354 millipascals⋅second. On the other hand, water vapor viscosity increases as temperature increases.

The viscosity of water is low, yet it is higher than that of most other liquids made of comparable-sized molecules. This is due to hydrogen bonding between neighboring water molecules.

Newtonian and Non-Newtonian Fluids

Newton’s law of friction is an important equation relating to viscosity.

τ = μ dc / dy = μ γ

τ = shearing stress in fluid (N/m 2 )

μ = dynamic viscosity of fluid (N s/m 2 )

dc = unit velocity (m/s)

dy = unit distance between layers (m)

γ  = dc / dy = shear rate (s -1 )

Rearranging the terms, gives the formula for dynamic viscosity:

μ  =  τ dy / dc  = τ  / γ    

A Newtonian fluid is a fluid that obeys Newton’s law of friction, where viscosity is independent of the strain rate. A non-Newtonian fluid is one which does not obey Newton’s law of friction. There are different ways non-Newtonian fluids deviate from Newtonian behavior:

• In shear-thinning fluids , viscosity decreases as the rate of shear strain increases. Ketchup is a good example of a shear-thinning fluid.
• In shear-thickening fluids , viscosity increases as the rate of shear strain increases. The suspension of silica particles in polyethylene glycol found in body armor and some brake pads is a shear-thickening fluid.
• In a thixotropic fluid , shaking or stirring reduces viscosity. Yogurt is an example of a thixotropic fluid.
• In a rheopectic or dilatant fluid , shaking or stirring increases viscosity. A mixture of cornstarch or water ( oobleck ) is a good example of a dilatant.
• Bingham plastics behave as solids normally, but flow as viscous liquid under high stress. Mayonnaise is an example of a Bingham plastic.

Measuring Viscosity

Instruments for measuring viscosity are viscometers and rheometers. Technically, a rheometer is a special type of viscometer. The devices either measure the flow of a fluid past a stationary object or else the movement of an object through a fluid. The viscosity value is the drag between the fluid and the object surface. These devices work when there is laminar flow and a small Reynold’s number.

• Assael, M. J.; et al. (2018). “Reference Values and Reference Correlations for the Thermal Conductivity and Viscosity of Fluids”. Journal of Physical and Chemical Reference Data . 47 (2): 021501. doi: 10.1063/1.5036625
• Balescu, Radu (1975). Equilibrium and Non-Equilibrium Statistical Mechanics . John Wiley & Sons. ISBN 978-0-471-04600-4.
• Bird, R. Bryon; Armstrong, Robert C.; Hassager, Ole (1987). Dynamics of Polymeric Liquids, Volume 1: Fluid Mechanics (2nd ed.). John Wiley & Sons.
• Cramer, M. S. (2012). “Numerical estimates for the bulk viscosity of ideal gases”. Physics of Fluids . 24 (6): 066102–066102–23. doi: 10.1063/1.4729611
• Hildebrand, Joel Henry (1977). Viscosity and Diffusivity: A Predictive Treatment . John Wiley & Sons. ISBN 978-0-471-03072-0.

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Viscosity is a physical quantity that describes a fluid’s resistance to flow. It is a property that resists the relative displacement of the different layers of the fluid. It can be considered as the fluid friction occurring inside the fluid due to the internal friction between the molecules. Viscosity is a primary factor in determining the forces to overcome when fluids are used in lubrication.

High Viscosity vs. Low Viscosity

Viscosity can be grouped into two categories based on fluid flow resistance – high and low. A high-viscosity fluid will be more viscous than a low-viscosity fluid. Fluids with low viscosity have a low resistance, shear quickly, and the molecules flow rapidly. On the other hand, high-viscosity fluids move languidly and resist deformation.

High-viscosity fluids include honey, pitch, molten glass, and peanut butter; low-viscosity fluids include air and water.

Dynamic and Kinematic Viscosity

There are two types of viscosity – dynamic and kinematic. Dynamic viscosity or absolute viscosity is the fluid’s resistance to motion when an external force is applied to shear the fluid. Kinematic viscosity is the resistive flow of fluid under the action of gravity.

Two fluids having the same dynamic viscosity can have different kinematic viscosities. The reason is that kinematic viscosity depends on the density of the fluid. On the other hand, density is not a factor with dynamic viscosity.

Dynamic Viscosity

Since viscosity measures the resistance of a fluid deformed by shear, it is expressed as the ratio of the shear stress to the velocity gradient.

η is the dynamic viscosity

F is the applied force

A is the area over which the force is applied

∂u/∂y is the velocity gradient

The above equation was derived by British mathematician Isaac Newton and is called Newton’s law of viscosity. It is applicable for straight, parallel, and uniform flow. The term u/v is the shear rate of deformation, and du/dv is the shear velocity.

Kinematic Viscosity

The ratio of the dynamic viscosity and fluid density gives the kinematic viscosity.

ν is the kinematic viscosity

ρ is the density

Symbols and Units

Greek symbol mu (μ) or eta (η) represents dynamic viscosity. Its SI unit is Pascal-second or Paˑs, equivalent to Nˑs/m 2 or Paˑs. The cgs unit is poise or P. ASTM standard uses centiPoise or cP.

1 P = 0.1 Paˑs and 1 cP = 0.001 Paˑs

Greek symbol nu (ν) represents kinematic viscosity. The SI unit of kinematic viscosity is m 2 /s. The cgs unit is Stokes or St. It is sometimes expressed in centiStokes.

1 St = 10 -4 m 2 /s and 1 cSt = 10 -6 m 2 /s

Viscosity Chart

Viscosity is measured using a viscometer. The following table gives the viscosity values of some common substances.

Chart Courtesy: Innovative Calibration Solutions

Factors Affecting Viscosity

The viscosity of liquids decreases quickly with an increase in temperature. On the other hand, the viscosity of gases increases with an increase in temperature. Thus, liquids flow more smoothly upon heating, and gasses flow more sluggishly.

The viscosity of gases is approximately proportional to the square root of temperature. The reason why gases increase their viscosity is because of an increased frequency of collisions. The more the molecules collide, the more disorganized they become. As a result, they move sluggishly.

Intermolecular forces in a fluid are a factor that affects viscosity. The higher the intermolecular forces, the higher the viscosity. Due to strong intermolecular forces, the fluid molecules are strongly bonded to each other. As a result, they are prevented from moving.

Newtonian and Non-Newtonian Fluid

It has been found that the viscosity is independent of the strain rates for a wide range of fluids. It means the viscosity remains constant no matter how much force is applied. Such a type of fluid is known as Newtonian fluid. The relationship between the viscosity and shear stress in a Newtonian fluid is linear. Examples are water, mineral oil, alcohol, and gasoline.

On the other hand, if the viscosity does not remain constant and depends on the force applied, the fluid is called non-Newtonian fluid. The viscosity changes as shear stress is applied. Examples include slime, toothpaste, cosmetics, and paints.

• Viscosity – Physics.info
• What is Viscosity in Physics? – Thoughtco.com
• Viscosity – Chem.libretexts.org
• Viscosity – Resources.saylor.org
• Viscosity Values Chart – Innocalsolutions.com

Article was last reviewed on Thursday, October 5, 2023

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definitions

Informally, viscosity is the quantity that describes a fluid's resistance to flow. Fluids resist the relative motion of immersed objects through them as well as to the motion of layers with differing velocities within them.

(dynamic) viscosity

Formally, viscosity (represented by the symbol η "eta") is the ratio of the shearing stress ( F / A ) to the velocity gradient ( ∆ v x /∆ y or dv x / dy ) in a fluid.

The more usual form of this relationship, called Newton's equation , states that the resulting shear of a fluid is directly proportional to the force applied and inversely proportional to its viscosity. The similarity to Newton's second law of motion ( F  =  ma ) should be apparent.

Or if you prefer calculus symbols (and who doesn't)…

The SI unit of viscosity is the pascal second [Pa s], which has no special name. Despite its self-proclaimed title as an international system, the International System of Units has had little international impact on viscosity. The pascal second is more rare than it should be in scientific and technical writing today. The most common unit of viscosity is the dyne second per square centimeter [dyne s/cm 2 ], which is given the name poise [P] after the French physiologist Jean Poiseuille (1799–1869). Ten poise equal one pascal second [Pa s] making the centipoise [cP] and millipascal second  [mPa s] identical.

kinematic viscosity

There are actually two quantities that are called viscosity. The quantity defined above is sometimes called dynamic viscosity , absolute viscosity , or simple viscosity to distinguish it from the other quantity, but is usually just called viscosity. The other quantity called kinematic viscosity (represented by the Greek letter ν "nu") is the ratio of the viscosity of a fluid to its density.

Kinematic viscosity is a measure of the resistive flow of a fluid under the influence of gravity. It is frequently measured using a device called a capillary viscometer — basically a graduated can with a narrow tube at the bottom. When two fluids of equal volume are placed in identical capillary viscometers and allowed to flow under the influence of gravity, the more viscous fluid takes longer than the less viscous fluid to flow through the tube. Capillary viscometers will be discussed in more detail later in this section.

The SI unit of kinematic viscosity is the square meter per second [m 2 /s], which has no special name. This unit is so large that it is rarely used. A more common unit of kinematic viscosity is the square centimeter per second [cm 2 /s], which is given the name stokes [St] after the Irish mathematician and physicist George Stokes (1819–1903). One square meter per second is equal to ten thousand stokes.

Even this unit is a bit too large, so the most common unit is probably the square millimeter per second [mm 2 /s] or the centistokes [cSt]. One square meter per second is equal to one million centistokes.

The stokes is a rare example of a word in the English language where the singular and plural forms are identical. Fish is the most immediate example of a aword that behaves like this. 1 fish, 2 fish, red fish, blue fish; 1 stokes, 2 stokes, some stokes, few stokes.

factors affecting viscosity

This part needs to be reorganized.

Viscosity is first and foremost a function of material. The viscosity of water at 20 °C is 1.0020 millipascal seconds (which is conveniently close to one by coincidence alone). Most ordinary liquids have viscosities on the order of 1 to 1000 mPa s, while gases have viscosities on the order of 1 to 10 μPa s. Pastes, gels, emulsions, and other complex liquids are harder to summarize. Some fats like butter or margarine are so viscous that they seem more like soft solids than like flowing liquids. Molten glass is extremely viscous and approaches infinite viscosity as it solidifies. Since the process is not as well defined as true freezing, some believe (incorrectly) that glass may still flow even after it has completely cooled, but this is not the case. At ordinary temperatures, glasses are as solid as true solids.

From everyday experience, it should be common knowledge that viscosity varies with temperature. Honey and syrups can be made to flow more readily when heated. Engine oil and hydraulic fluids thicken appreciably on cold days and significantly affect the performance of cars and other machinery during the winter months. In general, the viscosity of a simple liquid decreases with increasing temperature. As temperature increases, the average speed of the molecules in a liquid increases and the amount of time they spend "in contact" with their nearest neighbors decreases. Thus, as temperature increases, the average intermolecular forces decrease. The actual manner in which the two quantities vary is nonlinear and changes abruptly when the liquid changes phase.

Viscosity is normally independent of pressure, but liquids under extreme pressure often experience an increase in viscosity. Since liquids are normally incompressible, an increase in pressure doesn't really bring the molecules significantly closer together. Simple models of molecular interactions won't work to explain this behavior and, to my knowledge, there is no generally accepted more complex model that does. The liquid phase is probably the least well understood of all the phases of matter.

While liquids get runnier as they get hotter, gases get thicker. (If one can imagine a "thick" gas.) The viscosity of gases increases as temperature increases and is approximately proportional to the square root of temperature. This is due to the increase in the frequency of intermolecular collisions at higher temperatures. Since most of the time the molecules in a gas are flying freely through the void, anything that increases the number of times one molecule is in contact with another will decrease the ability of the molecules as a whole to engage in the coordinated movement. The more these molecules collide with one another, the more disorganized their motion becomes. Physical models, advanced beyond the scope of this book, have been around for nearly a century that adequately explain the temperature dependence of viscosity in gases. Newer models do a better job than the older models. They also agree with the observation that the viscosity of gases is roughly independent of pressure and density. The gaseous phase is probably the best understood of all the phases of matter.

Since viscosity is so dependent on temperature, it shouldn't never be stated without it.

This is a pretty good model for liquids…

η =  Ae B / T

y  =  b  +  mx

Motor oil is like every other fluid in that its viscosity varies with temperature and pressure. Since the conditions under which most automobiles will be operated can be anticipated, the behavior of motor oil can be specified in advance. In the United States, the organization that sets the standards for the performance of motor oils is the Society of Automotive Engineers (SAE). The SAE numbering scheme describes the behavior of motor oils under low and high temperature conditions — conditions that correspond to starting and operating temperatures. The first number, which is always followed by the letter W for winter, describes the low temperature behavior of the oil at start up while the second number describes the high temperature behavior of the oil after the engine has been running for some time. Lower SAE numbers describe oils that are meant to be used under lower temperatures. Oils with low SAE numbers are generally runnier (less viscous) than oils with high SAE numbers, which tend to be thicker (more viscous).

For example, 10W‑40 oil would have a viscosity no greater than 7,000 mPa s in a cold engine crankcase even if its temperature should drop to −25 °C on a cold winter night and a viscosity no less than 2.9 mPa s in the high pressure parts of an engine near the point of overheating (150 °C).

capillary viscometer

The the mathematical expression describing the flow of fluids in circular tubes was determined by the French physician and physiologist Jean Poiseuille (1799–1869). Since it was also discovered independently by the German hydraulic engineer Gotthilf Hagen (1797–1884), it should be properly known as the Hagen-Poiseuille equation , but it is usually just called Poiseuille's equation . I will not derive it here (but I probably should someday). For non-turbulent, non-pulsatile fluid flow through a uniform straight pipe, the volume flow rate ( q m ) is…

• directly proportional to the pressure difference ( ∆ P ) between the ends of the tube
• inversely proportional to the length ( ℓ ) of the tube
• inversely proportional to the viscosity ( η ) of the fluid
• proportional to the fourth power of the radius ( r 4 ) of the tube

Solve for viscosity if that's what you want to know.

Capillary viscometer… keep writing… sorry this is incomplete.

falling sphere

The mathematical expression describing the viscous drag force on a sphere was determined by the 19th century British physicist George Stokes . I will not derive it here (but I probably should someday in the future).

R  = 6πη rv

The formula for the buoyant force on a sphere is accredited to the Ancient Greek engineer Archimedes of Syracuse , but equations weren't invented back then.

B  = ρ fluid gV displaced

The formula for weight had to be invented by someone, but I don't know who.

W  =  mg  = ρ object gV object

Let's combine all these things together for a sphere falling in a fluid. Weight points down, buoyancy points up, drag points up. After a while, the sphere will fall with constant velocity. When it does, all these forces cancel. When a sphere is falling through a fluid it is completely submerged, so there is only one volume to talk about — the volume of a sphere. Let's work through this.

And here we are.

Drop a sphere into a liquid. If you know the size and density of the sphere and the density of the liquid, you can determine the viscosity of the liquid. If you don't know the density of the liquid you can still determine the kinematic viscosity. If you don't know the density of the sphere, but you know its mass and radius, well then you can calculate its density.

non-newtonian fluids

Newton's equation relates shear stress and velocity gradient by means of a quantity called viscosity. A newtonian fluid is one in which the viscosity is just a number. A non-newtonian fluid is one in which the viscosity is a function of some mechanical variable like shear stress or time. Non-newtonian fluids that change over time are said to have a memory .

Some gels and pastes behave like a fluid when worked or agitated and then settle into a nearly solid state when at rest. Such materials are examples of shear-thinning fluids. House paint is a shear-thinning fluid and it's a good thing, too. Brushing, rolling, or spraying are means of temporarily applying shear stress. This reduces the paint's viscosity to the point where it can now flow out of the applicator and onto the wall or ceiling. Once this shear stress is removed the paint returns to its resting viscosity, which is so large that an appropriately thin layer behaves more like a solid than a liquid and the paint does not run or drip. Think about what it would be like to paint with water or honey for comparison. The former is always too runny and the latter is always too sticky.

Toothpaste is another example of a material whose viscosity decreases under stress. Toothpaste behaves like a solid while it sits at rest inside the tube. It will not flow out spontaneously when the cap is removed, but it will flow out when you put the squeeze on it. Now it ceases to behave like a solid and starts to act like a thick liquid. when it lands on your toothbrush, the stress is released and the toothpaste returns to a nearly solid state. You don't have to worry about it flowing off the brush as you raise it to your mouth.

Shear-thinning fluids can be classified into one of three general groups. A material that has a viscosity that decreases under shear stress but stays constant over time is said to be pseudoplastic . A material that has a viscosity that decreases under shear stress and then continues to decrease with time is said to be thixotropic . If the transition from high viscosity (nearly semisolid) to low viscosity (essentially liquid) takes place only after the shear stress exceeds some minimum value, the material is said to be a bingham plastic .

Materials that thicken when worked or agitated are called shear-thickening fluids . An example that is often shown in science classrooms is a paste made of cornstarch and water (mixed in the correct proportions). The resulting bizarre goo behaves like a liquid when squeezed slowly and an elastic solid when squeezed rapidly. Ambitious science demonstrators have filled tanks with the stuff and then run across it. As long as they move quickly the surface acts like a block of solid rubber, but the instant they stop moving the paste behaves like a liquid and the demonstrator winds up taking a cornstarch bath. The shear-thickening behavior makes it a difficult bath to get out of. The harder you work to get out, the harder the material pulls you back in. The only way to escape it is to move slowly.

Materials that turn nearly solid under stress are more than just a curiosity. They're ideal candidates for body armor and protective sports padding. A bulletproof vest or a kneepad made of of shear-thickening material would be supple and yielding to the mild stresses of ordinary body motions, but would turn rock hard in response to the traumatic stress imposed by a weapon or a fall to the ground.

Shear-thickening fluids are are also divided into two groups: those with a time-dependent viscosity (memory materials) and those with a time-independent viscosity (non-memory materials). If the increase in viscosity increases over time, the material is said to be rheopectic . If the increase is roughly directly proportional to the shear stress and does not change over time, the material is said to be dilatant .

With a bit of adjustment, Newton's equation can be written as a power law that handles the pseudoplastics and the dilantants — the Ostwald-de Waele equation …

where η the viscosity is replaced with k the flow consistency index [Pa s n ] and the velocity gradient is raised to some power n called the flow behavior index [dimensionless]. The latter number varies with the class of fluid.

A different modification to Newton's equation is needed to handle Bingham plastics — the Bingham equation …

where σ y is the yield stress [Pa] and η pl is the plastic viscosity [Pa s]. The former number separates Bingham plastics from newtonian fluids.

Combining the Ostwald-de Waele power law with the Bingham yield stress gives us the more general Herschel-Bulkley equation …

where again, σ y is the yield stress [Pa], k is the flow consistency index [Pa s n ], and n is the flow behavior index [dimensionless].

viscoelasticity

When a force ( F ) is applied to an object, one of four things can happen.

F  =  ma

This term is not interesting to us right now. We've already discussed this kind of behavior in earlier chapters. Mass ( m ) is resistance to acceleration ( a ), which is the second derivative of position ( x ). Let's move on to something new.

F  = − bv

This is the simplified model where drag is directly proportional to speed ( v ), the first derivative of position ( x ). We used this in terminal velocity problems just because it gave differential equations that were easy to solve. We also used it in the damped harmonic oscillator, again because it gave differential equations that were easy to solve (relatively easy, anyway). The proportionality constant ( b ) is often called the damping factor.

F  = − kx

The proportionality constant ( k ) is the spring constant. Position ( x ) is not the part of any derivative nor is it raised to any power.

F  = − f

That symbol f makes it look like we're discussing static friction. In fluids (non-newtonian fluids, to be specific) a term like this is associated with yield stress. Position ( x ) is not involved in any way.

Put everything together and state acceleration and velocity as derivatives of position.

This differential equation summarizes the possible behaviors of an object. The interesting thing is that it mixes up the behaviors of fluids and solids. The more interesting thing is that there are occasions when both behaviors will be present in one thing. Materials that both flow like fluids and deform like solids are said to be viscoelastic — an obvious mash-up of viscosity and elasticity. The study of materials with fluid and solid properties is called rheology , which comes from the Greek verb ρέω ( reo ), to flow.

What old book gave me this idea? What should I write next?

Foods generally exhibit what is called viscoelastic behaviour, whereby a mix of the characteristic elastic properties of solids and flow properties of liquids are both found to varying extents

• Cheese pull occurs when melting fats lubricate linked protein strands. The fats flow like a liquid and the proteins stretch like a solid.

Viscosity refers to a fluid's resistance to flow. Fluids with high viscosity, like honey, flow more slowly than low-viscosity fluids, like water.

Think of a race between two people - one is running through air (like water flowing), and the other is trying to run through a pool of honey. The person in the honey will move slower because of the 'resistance' or 'drag' they experience. That's what we mean when we talk about viscosity!

Related terms

Newtonian Fluid : A fluid whose viscosity remains constant, regardless of the forces acting upon it.

Non-Newtonian Fluid : A fluid whose viscosity changes depending on the force applied. Examples include ketchup or quicksand.

Shear Rate : This refers to how quickly a liquid’s particles move relative to each other. It can affect a liquid's apparent viscosity.

" Viscosity " appears in:

Subjects ( 2 ).

AP Physics 2

AP Physics C: Mechanics

Study guides ( 1 )

AP Chemistry - 3.3 Solids, Liquids, and Gases

Practice Questions ( 2 )

Higher viscosity is caused by _______.

What is viscosity?

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Have you ever noticed that some liquids like water flow very rapidly while some others like castor oil do not flow fast? Why is it so? Didn’t that question occur to you yet? Well, if it did, we have the answer to it! This is the concept of Viscosity. In this chapter, we will study all about the topic and look at the laws and examples of the same.

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It is the internal resistance to flow possessed by a liquid. The liquids which flow slowly, have high internal resistance. This is because of the strong intermolecular forces . Therefore, these liquids are more viscous and have high viscosity.

The liquids which flow rapidly have a low internal resistance . This is because of the weak intermolecular forces. Hence, they are less viscous or have low viscosity.

Laminar Flow

Consider a liquid flowing through a narrow tube. All parts of the liquids do not move through the tube with the same velocity. Imagine the liquid to be made up of a large number of thin cylindrical coaxial layers. The layers which are in contact with the walls of the tube are almost stationary. As we move from the wall towards the centre of the tube, the velocity of the cylindrical layers keeps on increasing till it is maximum at the centre.

This is a laminar flow. It is a type of flow with a regular gradation of velocity in going from one layer to the next. As we move from the centre towards the walls, the velocity of the layers keeps on decreasing. In other words , every layer offers some resistance or friction to the layer immediately below it.

Viscosity is the force of friction which one part of the liquid offers to another part of the liquid. The force of friction f between two layers each having area A sq cm, separated by a distance dx cm, and having a velocity difference of dv cm/sec, is given by:

f ∝ A ( dv / dx )

f = η A ( dv/dx)

where η  is a constant known as the coefficient of viscosity and dv/dx is called velocity gradient. If dx =1 , A = 1 sq cm; dv = 1 cm/sec, then f = η. Hence the coefficient of viscosity may be defined as the force of friction required to maintain a velocity difference of 1 cm/sec between two parallel layers, 1 cm apart and each having an area of 1 sq cm.

Browse more Topics under Mechanical Properties Of Fluids

• Streamline Flow
• Surface Tension
• Bernoulli’s Principle and Equation
• Pressure and Its Applications

Units of Viscosity

We know that: η = f .dx / A .dv. Hence, η = dynes × cm / cm 2  ×cm/sec. Therefore we may write: η = dynes cm -2  sec or the units of viscosity are dynes sec cm -2 . This quantity is called 1 Poise.

f = m × a η = (m × a × dx) / ( A .dv) Hence, η = g cm -1  s -1 Therefore, η = 1 poise

In S.I. units, η = f .dx / A .dv =  N × m / ( m 2  ×ms -1 ) Therefore we may write, η = N m -2  or Pas

1 Poise = 1 g cm -1 s -1 = 0.1 kg m -1  s -1 

Solved Examples For You

Q: The space between two large horizontal metal plates 6 c m apart, is filled with a liquid of viscosity 0.8 N / m . A thin plate of surface area 0.01 m 2 is moved parallel to the length of the plate such that the plate is at a distance of 2 m from one of the plates and 4 c m from the other. If the plate moves with a constant speed of 1 m s − 1 , then:

• Fluid layer with the maximum velocity lies midway between the plates.
• The layer of the fluid, which is in contact with the moving plate, has the maximum velocity.
• That layer which is in contact with the moving plate and is on the side of the farther plate is moving with maximum velocity.
• Fluid in contact with the moving plate and which is on the side of the nearer plate is moving with maximum velocity.

Solution: B) The two horizontal plates are at rest. Also, the plate in between the two plates, is moving ahead with a constant speed of 1 m s − 1 . The layer closest to this plate will thus move with the maximum velocity.

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14.9: Viscosity and Turbulence

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Learning Objectives

• Explain what viscosity is
• Calculate flow and resistance with Poiseuille's law
• Explain how pressure drops due to resistance
• Calculate the Reynolds number for an object moving through a fluid
• Use the Reynolds number for a system to determine whether it is laminar or turbulent
• Describe the conditions under which an object has a terminal speed

In Applications of Newton’s Laws , which introduced the concept of friction, we saw that an object sliding across the floor with an initial velocity and no applied force comes to rest due to the force of friction. Friction depends on the types of materials in contact and is proportional to the normal force. We also discussed drag and air resistance in that same chapter. We explained that at low speeds, the drag is proportional to the velocity, whereas at high speeds, drag is proportional to the velocity squared. In this section, we introduce the forces of friction that act on fluids in motion. For example, a fluid flowing through a pipe is subject to resistance, a type of friction, between the fluid and the walls. Friction also occurs between the different layers of fluid. These resistive forces affect the way the fluid flows through the pipe.

Viscosity and Laminar Flow

When you pour yourself a glass of juice, the liquid flows freely and quickly. But if you pour maple syrup on your pancakes, that liquid flows slowly and sticks to the pitcher. The difference is fluid friction, both within the fluid itself and between the fluid and its surroundings. We call this property of fluids viscosity. Juice has low viscosity, whereas syrup has high viscosity.

The precise definition of viscosity is based on laminar, or nonturbulent, flow. Figure \(\PageIndex{1}\) shows schematically how laminar and turbulent flow differ. When flow is laminar, layers flow without mixing. When flow is turbulent, the layers mix, and significant velocities occur in directions other than the overall direction of flow.

Turbulence is a fluid flow in which layers mix together via eddies and swirls. It has two main causes. First, any obstruction or sharp corner, such as in a faucet, creates turbulence by imparting velocities perpendicular to the flow. Second, high speeds cause turbulence. The drag between adjacent layers of fluid and between the fluid and its surroundings can form swirls and eddies if the speed is great enough. In Figure \(\PageIndex{2}\), the speed of the accelerating smoke reaches the point that it begins to swirl due to the drag between the smoke and the surrounding air.

Figure \(\PageIndex{3}\) shows how viscosity is measured for a fluid. The fluid to be measured is placed between two parallel plates. The bottom plate is held fixed, while the top plate is moved to the right, dragging fluid with it. The layer (or lamina) of fluid in contact with either plate does not move relative to the plate, so the top layer moves at speed v while the bottom layer remains at rest. Each successive layer from the top down exerts a force on the one below it, trying to drag it along, producing a continuous variation in speed from v to 0 as shown. Care is taken to ensure that the flow is laminar, that is, the layers do not mix. The motion in the figure is like a continuous shearing motion. Fluids have zero shear strength, but the rate at which they are sheared is related to the same geometrical factors A and L as is shear deformation for solids. In the diagram, the fluid is initially at rest. The layer of fluid in contact with the moving plate is accelerated and starts to move due to the internal friction between moving plate and the fluid. The next layer is in contact with the moving layer; since there is internal friction between the two layers, it also accelerates, and so on through the depth of the fluid. There is also internal friction between the stationary plate and the lowest layer of fluid, next to the station plate. The force is required to keep the plate moving at a constant velocity due to the internal friction.

A force F is required to keep the top plate in Figure \(\PageIndex{3}\) moving at a constant velocity v, and experiments have shown that this force depends on four factors. First, F is directly proportional to v (until the speed is so high that turbulence occurs—then a much larger force is needed, and it has a more complicated dependence on v). Second, F is proportional to the area A of the plate. This relationship seems reasonable, since A is directly proportional to the amount of fluid being moved. Third, F is inversely proportional to the distance between the plates L. This relationship is also reasonable; L is like a lever arm, and the greater the lever arm, the less the force that is needed. Fourth, F is directly proportional to the coefficient of viscosity, \(\eta\) The greater the viscosity, the greater the force required. These dependencies are combined into the equation

\[F = \eta \frac{vA}{L} \ldotp\]

This equation gives us a working definition of fluid viscosity \(\eta\). Solving for \(\eta\) gives

\[\eta = \frac{FL}{vA} \label{14.17}\]

which defines viscosity in terms of how it is measured. The SI unit of viscosity is \(\frac{N\; \cdotp m}{[(m/s)m^{2}]}\) = (N/m 2 )s or Pa • s. Table \(\PageIndex{1}\) lists the coefficients of viscosity for various fluids. Viscosity varies from one fluid to another by several orders of magnitude. As you might expect, the viscosities of gases are much less than those of liquids, and these viscosities often depend on temperature.

Laminar Flow Confined to Tubes: Poiseuille’s Law

What causes flow? The answer, not surprisingly, is a pressure difference. In fact, there is a very simple relationship between horizontal flow and pressure. Flow rate \(Q\) is in the direction from high to low pressure. The greater the pressure differential between two points, the greater the flow rate. This relationship can be stated as

\[Q = \frac{p_{2} - p_{1}}{R}\]

where \(p_1\) and \(p_2\) are the pressures at two points, such as at either end of a tube, and \(R\) is the resistance to flow. The resistance \(R\) includes everything, except pressure, that affects flow rate. For example, \(R\) is greater for a long tube than for a short one. The greater the viscosity of a fluid, the greater the value of \(R\). Turbulence greatly increases R, whereas increasing the diameter of a tube decreases \(R\).

If viscosity is zero, the fluid is frictionless and the resistance to flow is also zero. Comparing frictionless flow in a tube to viscous flow, as in Figure \(\PageIndex{4}\), we see that for a viscous fluid, speed is greatest at midstream because of drag at the boundaries. We can see the effect of viscosity in a Bunsen burner flame [part (c)], even though the viscosity of natural gas is small.

The resistance R to laminar flow of an incompressible fluid with viscosity \(\eta\) through a horizontal tube of uniform radius r and length l, is given by

\[R = \frac{8 \eta l}{\pi r^{4}} \ldotp \label{14.18}\]

This equation is called Poiseuille’s law for resistance , named after the French scientist J. L. Poiseuille (1799–1869), who derived it in an attempt to understand the flow of blood through the body.

Let us examine Poiseuille’s expression for R to see if it makes good intuitive sense. We see that resistance is directly proportional to both fluid viscosity \(\eta\) and the length l of a tube. After all, both of these directly affect the amount of friction encountered—the greater either is, the greater the resistance and the smaller the flow. The radius r of a tube affects the resistance, which again makes sense, because the greater the radius, the greater the flow (all other factors remaining the same). But it is surprising that r is raised to the fourth power in Poiseuille’s law. This exponent means that any change in the radius of a tube has a very large effect on resistance. For example, doubling the radius of a tube decreases resistance by a factor of 2 4 = 16.

Taken together \(Q = \frac{p_{2} - p_{1}}{R}\) and \(R = \frac{8 \eta l}{\pi r^{4}}\) give the following expression for flow rate:

\[Q = \frac{(p_{2} - p_{1}) \pi r^{4}}{8 \eta l} \ldotp \label{14.19}\]

This equation describes laminar flow through a tube. It is sometimes called Poiseuille’s law for laminar flow, or simply Poiseuille’s law (Figure \(\PageIndex{5}\)).

Example 14.8: Using Flow Rate - Air Conditioning Systems

An air conditioning system is being designed to supply air at a gauge pressure of 0.054 Pa at a temperature of 20 °C. The air is sent through an insulated, round conduit with a diameter of 18.00 cm. The conduit is 20-meters long and is open to a room at atmospheric pressure 101.30 kPa. The room has a length of 12 meters, a width of 6 meters, and a height of 3 meters. (a) What is the volume flow rate through the pipe, assuming laminar flow? (b) Estimate the length of time to completely replace the air in the room. (c) The builders decide to save money by using a conduit with a diameter of 9.00 cm. What is the new flow rate?

Assuming laminar flow, Poiseuille’s law states that

\[Q = \frac{(p_{2} - p_{1}) \pi r^{4}}{8 \eta l} = \frac{dV}{dt} \ldotp \nonumber\]

We need to compare the artery radius before and after the flow rate reduction. Note that we are given the diameter of the conduit, so we must divide by two to get the radius.

• Assuming a constant pressure difference and using the viscosity \(\eta = 0.0181\; mPa\; \cdotp s\), $$Q = \frac{(0.054\; Pa)(3.14)(0.09\; m)^{4}}{8(0.0181 \times 10^{-3}\; Pa\; \cdotp s)(20\; m)} = 3.84 \times 10^{-3}\; m^{3}/s \ldotp$$
• Assuming constant flow \(Q = \frac{dV}{dt} \approx \frac{\Delta V}{\Delta t}\) $$\Delta t = \frac{\Delta V}{Q} = \frac{(12\; m)(6\; m)(3\; m)}{3.84 \times 10^{-3}\; m^{3}/s} = 5.63 \times 10^{4}\; s = 15.63\; hr \ldotp \nonumber$$
• Using laminar flow, Poiseuille’s law yields $$Q = \frac{(0.054\; Pa)(3.14)(0.045\; m){4}}{8(0.0181 \times 10^{-3}\; Pa\; \cdotp s)(20\; m)} = 22.40 \times 10^{-4}\; m^{3}/s \ldotp$$Thus, the radius of the conduit decreases by half reduces the flow rate to 6.25% of the original value.

Significance

In general, assuming laminar flow, decreasing the radius has a more dramatic effect than changing the length. If the length is increased and all other variables remain constant, the flow rate is decreased:

\[\begin{split} \frac{Q_{A}}{Q_{B}} & = \frac{\frac{(p_{2} - p_{1}) \pi r_{A}^{4}}{8 \eta l_{A}}}{\frac{(p_{2} - p_{1}) \pi r_{B}^{4}}{8 \eta l_{B}}} = \frac{l_{B}}{l_{A}} \\ Q_{B} & = \frac{l_{A}}{l_{B}} Q_{A} \ldotp \end{split} \nonumber\]

Doubling the length cuts the flow rate to one-half the original flow rate.

If the radius is decreased and all other variables remain constant, the volume flow rate decreases by a much larger factor.

\[\begin{split} \frac{Q_{A}}{Q_{B}} & = \frac{\frac{(p_{2} - p_{1}) \pi r_{A}^{4}}{8 \eta l_{A}}}{\frac{(p_{2} - p_{1}) \pi r_{B}^{4}}{8 \eta l_{B}}} = \left(\dfrac{r_{A}}{r_{B}}\right)^{4} \\ Q_{B} & = \left(\dfrac{r_{B}}{r_{A}}\right)^{4} Q_{A} \end{split}\]

Cutting the radius in half decreases the flow rate to one-sixteenth the original flow rate.

Flow and Resistance as Causes of Pressure Drops

Water pressure in homes is sometimes lower than normal during times of heavy use, such as hot summer days. The drop in pressure occurs in the water main before it reaches individual homes. Let us consider flow through the water main as illustrated in Figure \(\PageIndex{6}\). We can understand why the pressure p 1 to the home drops during times of heavy use by rearranging the equation for flow rate:

\[\begin{align} Q & = \frac{p_{2} - p_{1}}{R} \\[4pt] p_{2} - p_{1} & = RQ . \label{EQ5} \end{align}\]

In this case, \(p_2\) is the pressure at the water works and \(R\) is the resistance of the water main. During times of heavy use, the flow rate \(Q\) is large. This means that \(p_2 − p_1\) must also be large. Thus \(p_1\) must decrease. It is correct to think of flow and resistance as causing the pressure to drop from p 2 to p 1 . The equation p 2 − p 1 = RQ is valid for both laminar and turbulent flows.

We can also use Equation \ref{EQ5} to analyze pressure drops occurring in more complex systems in which the tube radius is not the same everywhere. Resistance is much greater in narrow places, such as in an obstructed coronary artery. For a given flow rate Q, the pressure drop is greatest where the tube is most narrow. This is how water faucets control flow. Additionally, R is greatly increased by turbulence, and a constriction that creates turbulence greatly reduces the pressure downstream. Plaque in an artery reduces pressure and hence flow, both by its resistance and by the turbulence it creates.

Measuring Turbulence

An indicator called the Reynolds number \(N_R\) can reveal whether flow is laminar or turbulent. For flow in a tube of uniform diameter, the Reynolds number is defined as

\[N_{R} = \frac{2 \rho vr}{\eta}\; (flow\; in\; tube) \label{14.20}\]

where \(\rho\) is the fluid density, v its speed, \(\eta\) its viscosity, and \(r\) the tube radius. The Reynolds number is a dimensionless quantity. Experiments have revealed that \(N_R\) is related to the onset of turbulence. For N R below about 2000, flow is laminar. For \(N_R\) above about 3000, flow is turbulent.

For values of \(N_R\) between about 2000 and 3000, flow is unstable—that is, it can be laminar, but small obstructions and surface roughness can make it turbulent, and it may oscillate randomly between being laminar and turbulent. In fact, the flow of a fluid with a Reynolds number between 2000 and 3000 is a good example of chaotic behavior. A system is defined to be chaotic when its behavior is so sensitive to some factor that it is extremely difficult to predict. It is difficult, but not impossible, to predict whether flow is turbulent or not when a fluid’s Reynold’s number falls in this range due to extremely sensitive dependence on factors like roughness and obstructions on the nature of the flow. A tiny variation in one factor has an exaggerated (or nonlinear) effect on the flow.

Example 14.9: Using Flow Rate - Turbulent Flow or Laminar Flow

In Example 14.8, we found the volume flow rate of an air conditioning system to be Q = 3.84 x 10 −3 m 3 /s. This calculation assumed laminar flow.

• Was this a good assumption?
• At what velocity would the flow become turbulent?

To determine if the flow of air through the air conditioning system is laminar, we first need to find the velocity, which can be found by

\[Q = Av = \pi r^{2} v \ldotp \nonumber\]

Then we can calculate the Reynold’s number, using the equation below, and determine if it falls in the range for laminar flow

\[R = \frac{2 \rho vr}{\eta} \ldotp \nonumber \]

• Using the values given: $$\begin{split} v & = \frac{Q}{\pi r^{2}} = \frac{3.84 \times 10^{-3}\; m^{3}/s}{3.14 (0.09\; m)^{2}} = 0.15\; m/s \\ R & = \frac{2 \rho vr}{\eta} = \frac{2 (1.23\; kg/m^{3})(0.15\; m/s)(0.09\; m)}{0.0181 \times 10^{-3}\; Pa\; \cdotp s} = 1835 \ldotp \end{split}$$Since the Reynolds number is 1835 < 2000, the flow is laminar and not turbulent. The assumption that the flow was laminar is valid.
• To find the maximum speed of the air to keep the flow laminar, consider the Reynold’s number. $$\begin{split} R & = \frac{2 \rho vr}{\eta} \leq 2000 \\ v & = \frac{2000(0.0181 \times 10^{-3}\; Pa\; \cdotp s)}{2(1.23\; kg/m^{3})(0.09\; m)} = 0.16\; m/s \ldotp \end{split}$$

When transferring a fluid from one point to another, it desirable to limit turbulence. Turbulence results in wasted energy, as some of the energy intended to move the fluid is dissipated when eddies are formed. In this case, the air conditioning system will become less efficient once the velocity exceeds 0.16 m/s, since this is the point at which turbulence will begin to occur.

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Definition of viscosity

called also coefficient of viscosity

• consistence
• consistency

Examples of viscosity in a Sentence

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'viscosity.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History

Middle English viscosite , from Anglo-French viscosité , from Medieval Latin viscositat-, viscositas , from Late Latin viscosus viscous

14th century, in the meaning defined at sense 1

Phrases Containing viscosity

• coefficient of viscosity
• viscosity index

Dictionary Entries Near viscosity

viscosimetrically

viscosity breaking

Cite this Entry

“Viscosity.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/viscosity. Accessed 18 May. 2024.

Kids Definition

Kids definition of viscosity, medical definition, medical definition of viscosity, more from merriam-webster on viscosity.

Nglish: Translation of viscosity for Spanish Speakers

Britannica English: Translation of viscosity for Arabic Speakers

Britannica.com: Encyclopedia article about viscosity

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• Properties Of Fluids
• Newtons Law Of Viscosity

Newton’s Law of Viscosity

Statement of newton’s law of viscosity.

According to Newton’s law of viscosity

The shear stress is directly proportional to the velocity gradient. The shear stress between the two adjacent layers of the fluid is directly proportional to the negative value of the velocity gradient between the same two adjacent layers of the fluid.

Mathematically, it is represented as:

Where μ is the constant of proportionality known as dynamic viscosity whose unit id N.s.m -2 .

Types of Fluids

There are two types of fluids based on Newton’s law of viscosity:

• Newtonian fluids
• Non-Newtonian fluids

Newtonian Fluids

The fluid whose viscosity remains constant is known as the Newtonian fluid. These fluids are independent of the amount of shear stress applied to them with respect to time. The relationship between the viscosity and shear stress of these fluids is linear.

Examples of Newtonian Fluids

• Mineral oil

Similar reads:

• SI unit of viscosity
• Determination of coefficient of viscosity of a given viscous liquid

Non-Newtonian Fluids

The fluid whose viscosity changes when shear stress is applied is known as the Non-Newtonian fluids. These fluids are the opposite of Newtonian fluids.

Examples of Non-Newtonian Fluids

Types of non-newtonian fluids.

There are four types of Non-Newtonian fluids, and they are:

• Dilatant: The viscosity of these fluids increases when shear stress is applied. Quicksand, cornflour with water, and putty are examples of dilatant fluids.
• Pseudoplastic: The viscosity of these fluids decreases when shear stress is applied. These fluids are the opposite of dilatant fluids. Ketchup is an example of pseudoplastic.
• Rheopectic: The viscosity of these fluids increases when shear stress is applied along with time. They are similar to dilatant fluids, however, these fluids are time-dependent. Cream and gypsum paste are examples of rheopectic fluids.
• Thixotropic: The viscosity of these fluids decreases when shear stress is applied along with time. Cosmetics and paint are examples of thixotropic fluids.

The other way of categorizing the Non-Newtonian fluids are based on their shear stress or the shear rate behaviour:

• The fluids whose shear stress is dependent on the time
• The fluids whose shear stress is independent of the time

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Frequently Asked Questions – FAQs

What is the unit of consistency index k.

The unit of consistency index K is N.sn/m2.

What happens to the shear stress in case of a rheopectic fluid?

In rheopectic fluid, the shear stress increases with time.

Give the equation that is used for explaining the pseudoplastic and dilatant fluids

The following is the equation that is used for explaining the pseudoplastic and dilatant fluids: \(\begin{array}{l}\tau =\mu (-\frac{dv}{dy})^{n}\end{array} \)

Give the equation that represents a Bingham plastic fluid, if the apparent viscosity is given as μ.

The equation that represents a Bingham plastic fluid, if the apparent viscosity is given as μ is given as below: \(\begin{array}{l}\tau =\mu (-\frac{dv}{dy})+\tau _{y}\end{array} \)

What is the value of flow behaviour index n for a pseudoplastic fluid?

The value of flow behaviour index n for a pseudoplastic fluid is

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11.4: Intermolecular Forces in Action- Surface Tension, Viscosity, and Capillary Action

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Learning Objectives

• To describe the unique properties of liquids.

Although you have been introduced to some of the interactions that hold molecules together in a liquid, we have not yet discussed the consequences of those interactions for the bulk properties of liquids. We now turn our attention to three unique properties of liquids that intimately depend on the nature of intermolecular interactions:

• surface tension,
• capillary action, and

Surface Tension

If liquids tend to adopt the shapes of their containers, then why do small amounts of water on a freshly waxed car form raised droplets instead of a thin, continuous film? The answer lies in a property called surface tension , which depends on intermolecular forces. Surface tension is the energy required to increase the surface area of a liquid by a unit amount and varies greatly from liquid to liquid based on the nature of the intermolecular forces, e.g., water with hydrogen bonds has a surface tension of 7.29 x 10 -2 J/m 2 (at 20°C), while mercury with metallic bonds has as surface tension that is 15 times higher: 4.86 x 10 -1 J/m 2 (at 20°C).

Figure \(\PageIndex{1}\) presents a microscopic view of a liquid droplet. A typical molecule in the interior of the droplet is surrounded by other molecules that exert attractive forces from all directions. Consequently, there is no net force on the molecule that would cause it to move in a particular direction. In contrast, a molecule on the surface experiences a net attraction toward the drop because there are no molecules on the outside to balance the forces exerted by adjacent molecules in the interior. Because a sphere has the smallest possible surface area for a given volume, intermolecular attractive interactions between water molecules cause the droplet to adopt a spherical shape. This maximizes the number of attractive interactions and minimizes the number of water molecules at the surface. Hence raindrops are almost spherical, and drops of water on a waxed (nonpolar) surface, which does not interact strongly with water, form round beads. A dirty car is covered with a mixture of substances, some of which are polar. Attractive interactions between the polar substances and water cause the water to spread out into a thin film instead of forming beads.

The same phenomenon holds molecules together at the surface of a bulk sample of water, almost as if they formed a skin. When filling a glass with water, the glass can be overfilled so that the level of the liquid actually extends above the rim. Similarly, a sewing needle or a paper clip can be placed on the surface of a glass of water where it “floats,” even though steel is much denser than water. Many insects take advantage of this property to walk on the surface of puddles or ponds without sinking. This is even observable in the zero gravity conditions of space as shown in Figure \(\PageIndex{2}\) (and more so in the video link) where water wrung from a wet towel continues to float along the towel's surface!

Such phenomena are manifestations of surface tension, which is defined as the energy required to increase the surface area of a liquid by a specific amount. Surface tension is therefore measured as energy per unit area, such as joules per square meter (J/m 2 ) or dyne per centimeter (dyn/cm), where 1 dyn = 1 × 10 −5 N. The values of the surface tension of some representative liquids are listed in Table \(\PageIndex{1}\). Note the correlation between the surface tension of a liquid and the strength of the intermolecular forces: the stronger the intermolecular forces, the higher the surface tension. For example, water, with its strong intermolecular hydrogen bonding, has one of the highest surface tension values of any liquid, whereas low-boiling-point organic molecules, which have relatively weak intermolecular forces, have much lower surface tensions. Mercury is an apparent anomaly, but its very high surface tension is due to the presence of strong metallic bonding.

Adding soaps and detergents that disrupt the intermolecular attractions between adjacent water molecules can reduce the surface tension of water. Because they affect the surface properties of a liquid, soaps and detergents are called surface-active agents, or surfactants. In the 1960s, US Navy researchers developed a method of fighting fires aboard aircraft carriers using “foams,” which are aqueous solutions of fluorinated surfactants. The surfactants reduce the surface tension of water below that of fuel, so the fluorinated solution is able to spread across the burning surface and extinguish the fire. Such foams are now used universally to fight large-scale fires of organic liquids.

Capillary Action

Intermolecular forces also cause a phenomenon called capillary action, which is the tendency of a polar liquid to rise against gravity into a small-diameter tube (a capillary ), as shown in Figure \(\PageIndex{3}\). When a glass capillary is is placed in liquid water, water rises up into the capillary. The height to which the water rises depends on the diameter of the tube and the temperature of the water but not on the angle at which the tube enters the water. The smaller the diameter, the higher the liquid rises.

• Cohesive forces bind molecules of the same type together
• Adhesive forces bind a substance to a surface

Capillary action is the net result of two opposing sets of forces: cohesive forces, which are the intermolecular forces that hold a liquid together, and adhesive forces, which are the attractive forces between a liquid and the substance that composes the capillary. Water has both strong adhesion to glass, which contains polar SiOH groups, and strong intermolecular cohesion. When a glass capillary is put into water, the surface tension due to cohesive forces constricts the surface area of water within the tube, while adhesion between the water and the glass creates an upward force that maximizes the amount of glass surface in contact with the water. If the adhesive forces are stronger than the cohesive forces, as is the case for water, then the liquid in the capillary rises to the level where the downward force of gravity exactly balances this upward force. If, however, the cohesive forces are stronger than the adhesive forces, as is the case for mercury and glass, the liquid pulls itself down into the capillary below the surface of the bulk liquid to minimize contact with the glass (Figure \(\PageIndex{4}\)). The upper surface of a liquid in a tube is called the meniscus, and the shape of the meniscus depends on the relative strengths of the cohesive and adhesive forces. In liquids such as water, the meniscus is concave; in liquids such as mercury, however, which have very strong cohesive forces and weak adhesion to glass, the meniscus is convex (Figure \(\PageIndex{4}\)).

Polar substances are drawn up a glass capillary and generally have a concave meniscus.

Fluids and nutrients are transported up the stems of plants or the trunks of trees by capillary action. Plants contain tiny rigid tubes composed of cellulose, to which water has strong adhesion. Because of the strong adhesive forces, nutrients can be transported from the roots to the tops of trees that are more than 50 m tall. Cotton towels are also made of cellulose; they absorb water because the tiny tubes act like capillaries and “wick” the water away from your skin. The moisture is absorbed by the entire fabric, not just the layer in contact with your body.

Viscosity (η) is the resistance of a liquid to flow. Some liquids, such as gasoline, ethanol, and water, flow very readily and hence have a low viscosity . Others, such as motor oil, molasses, and maple syrup, flow very slowly and have a high viscosity . The two most common methods for evaluating the viscosity of a liquid are (1) to measure the time it takes for a quantity of liquid to flow through a narrow vertical tube and (2) to measure the time it takes steel balls to fall through a given volume of the liquid. The higher the viscosity, the slower the liquid flows through the tube and the steel balls fall. Viscosity is expressed in units of the poise (mPa•s); the higher the number, the higher the viscosity. The viscosities of some representative liquids are listed in Table 11.3.1 and show a correlation between viscosity and intermolecular forces. Because a liquid can flow only if the molecules can move past one another with minimal resistance, strong intermolecular attractive forces make it more difficult for molecules to move with respect to one another. The addition of a second hydroxyl group to ethanol, for example, which produces ethylene glycol (HOCH 2 CH 2 OH), increases the viscosity 15-fold. This effect is due to the increased number of hydrogen bonds that can form between hydroxyl groups in adjacent molecules, resulting in dramatically stronger intermolecular attractive forces.

There is also a correlation between viscosity and molecular shape. Liquids consisting of long, flexible molecules tend to have higher viscosities than those composed of more spherical or shorter-chain molecules. The longer the molecules, the easier it is for them to become “tangled” with one another, making it more difficult for them to move past one another. London dispersion forces also increase with chain length. Due to a combination of these two effects, long-chain hydrocarbons (such as motor oils) are highly viscous.

Viscosity increases as intermolecular interactions or molecular size increases.

Video Discussing Surface Tension and Viscosity. Video Link: Surface Tension, Viscosity, & Melting Point, YouTube(opens in new window) [youtu.be]

Application: Motor Oils

Motor oils and other lubricants demonstrate the practical importance of controlling viscosity. The oil in an automobile engine must effectively lubricate under a wide range of conditions, from subzero starting temperatures to the 200°C that oil can reach in an engine in the heat of the Mojave Desert in August. Viscosity decreases rapidly with increasing temperatures because the kinetic energy of the molecules increases, and higher kinetic energy enables the molecules to overcome the attractive forces that prevent the liquid from flowing. As a result, an oil that is thin enough to be a good lubricant in a cold engine will become too “thin” (have too low a viscosity) to be effective at high temperatures.

The viscosity of motor oils is described by an SAE (Society of Automotive Engineers) rating ranging from SAE 5 to SAE 50 for engine oils: the lower the number, the lower the viscosity (Figure \(\PageIndex{5}\)). So-called single-grade oils can cause major problems. If they are viscous enough to work at high operating temperatures (SAE 50, for example), then at low temperatures, they can be so viscous that a car is difficult to start or an engine is not properly lubricated. Consequently, most modern oils are multigrade , with designations such as SAE 20W/50 (a grade used in high-performance sports cars), in which case the oil has the viscosity of an SAE 20 oil at subzero temperatures (hence the W for winter) and the viscosity of an SAE 50 oil at high temperatures. These properties are achieved by a careful blend of additives that modulate the intermolecular interactions in the oil, thereby controlling the temperature dependence of the viscosity. Many of the commercially available oil additives “for improved engine performance” are highly viscous materials that increase the viscosity and effective SAE rating of the oil, but overusing these additives can cause the same problems experienced with highly viscous single-grade oils.

Example \(\PageIndex{1}\)

Based on the nature and strength of the intermolecular cohesive forces and the probable nature of the liquid–glass adhesive forces, predict what will happen when a glass capillary is put into a beaker of SAE 20 motor oil. Will the oil be pulled up into the tube by capillary action or pushed down below the surface of the liquid in the beaker? What will be the shape of the meniscus (convex or concave)? (Hint: the surface of glass is lined with Si–OH groups.)

Given: substance and composition of the glass surface

Asked for: behavior of oil and the shape of meniscus

• Identify the cohesive forces in the motor oil.
• Determine whether the forces interact with the surface of glass. From the strength of this interaction, predict the behavior of the oil and the shape of the meniscus.

A Motor oil is a nonpolar liquid consisting largely of hydrocarbon chains. The cohesive forces responsible for its high boiling point are almost solely London dispersion forces between the hydrocarbon chains.

B Such a liquid cannot form strong interactions with the polar Si–OH groups of glass, so the surface of the oil inside the capillary will be lower than the level of the liquid in the beaker. The oil will have a convex meniscus similar to that of mercury.

Exercise \(\PageIndex{1}\)

Predict what will happen when a glass capillary is put into a beaker of ethylene glycol. Will the ethylene glycol be pulled up into the tube by capillary action or pushed down below the surface of the liquid in the beaker? What will be the shape of the meniscus (convex or concave)?

Capillary action will pull the ethylene glycol up into the capillary. The meniscus will be concave.

Surface tension, capillary action, and viscosity are unique properties of liquids that depend on the nature of intermolecular interactions. Surface tension is the energy required to increase the surface area of a liquid by a given amount. The stronger the intermolecular interactions, the greater the surface tension. Surfactants are molecules, such as soaps and detergents, that reduce the surface tension of polar liquids like water. Capillary action is the phenomenon in which liquids rise up into a narrow tube called a capillary. It results when cohesive forces , the intermolecular forces in the liquid, are weaker than adhesive forces , the attraction between a liquid and the surface of the capillary. The shape of the meniscus , the upper surface of a liquid in a tube, also reflects the balance between adhesive and cohesive forces. The viscosity of a liquid is its resistance to flow. Liquids that have strong intermolecular forces tend to have high viscosities.

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